Coupled superconducting charge quantum bit device and controlled-not gate using the same

ABSTRACT

A control quantum bit circuit and a target quantum bit circuit each have a quantum box electrode including a superconductor, a counter electrode coupled to the quantum box electrode through a tunnel barrier, and a gate electrode coupled to the quantum box electrode through a gate capacitor. The quantum box electrode of the control quantum bit circuit is coupled to the quantum box electrode of the target quantum bit circuit through a box-electrode coupling capacitor.

This application claims priority to prior Japanese patent application JP2003-286640, the disclosure of which is incorporated herein byreference.

BACKGROUND OF THE INVENTION

The present invention relates to a method for implementing a logicoperation in quantum computing devices constructed by Josephson coupledsystems.

Quantum computers are new computers actively using the basic principleof quantum mechanics. The quantum computer can solve a specific problem,for example, the prime factorization of large natural numbers, muchfaster than conventional classical computers can do. The quantumcomputer uses a quantum two-level system, called a quantum bit,corresponding to a bit used in the classical computer.

In other words, the basic unit of the information in the quantumcomputer is defined by a quantum bit (qubit). A qubit corresponds to,for example, an atom (ion) having different quantum states. Two of thequantum states are used to store digital information.

There are candidates for quantum two-level systems. From the viewpointof quantum bit integration, solid-state devices are promising. A quantumbit using a superconducting device has good coherence. Accordingly, thequantum bit using the superconducting device holds a big lead in thesolid-state devices.

Japanese Unexamined Patent Application Publication No. 2000-277723(herein below, referred to as Patent Document 1) discloses a quantumcomputing device whereby it is unnecessary to extract high-speedsignals, thus easily reading out the result of a computation. In thequantum computing device, a quantum bit is formed by a quantum boxelectrode and a counter electrode, or formed by a superconducting boxelectrode and a superconducting counter electrode. The quantum bit iscontrolled by a gate voltage that is applied to a gate electrode. Aprobe electrode is coupled to the quantum bit via a tunnel barrier. Theprobe electrode can read out the state of the quantum bit aftercomputation and also can prepare the initial state thereof beforecomputation. An electrostatic potential of the superconducting boxelectrode is controlled by the gate voltage applied to the gateelectrode. Thus, a transition In Cooper-pair tunneling through thetunnel barrier, namely, the state of the quantum bit is controlled. Theprobe electrode is biased to a positive voltage. So long as at least oneexcess Cooper pair exists in the superconducting box electrode, theprobe electrode extracts two electrons with two quasiparticle tunnelingevents through the tunnel barrier to observe the state of the quantumbit.

The Cooper pair will now be described. In normal metals, a weak Coulombrepulsion acts between electrons. Electrons move independently of eachother. On the other hand, when an attractive interaction acts betweenelectrons even slightly, an energy produced by a pair of electrons, ofwhich momentums are equal in size and opposite in direction, is lowerthan that produced by electrons moving independently of each other. Thepair of electrons is called a Cooper pair. In metals in each of whichthe attractive interaction acts between electrons, when energy saved bygenerating Cooper pairs is higher than that of thermal agitation, manyelectrons are paired, thus condensing into one energy state. This statecorresponds to superconductivity. The phenomenon of perfect diamagnetism(Meissner effect) is explained based on the fact that the condensedCooper pairs have the same phase and all of the Cooper pairs can bedescribed by one wave function.

A quasiparticle will now be described. In a superconducting metal, manyelectrons are paired as Cooper pairs and are condensed into one energystate. When energy (superconducting gap energy) of a predetermined levelor more caused by lattice vibration or external light irradiation isapplied to the Cooper pairs, each Cooper pair is broken into twoelectrons. The electrons are in a superconductor excited state. Thestate of each of the two electrons is different from that of a freeelectron in a normal metal. Therefore, the electron In this state iscalled a quasiparticle in order to distinguish from the normal freeelectron. In a tunnel function including two superconducting electrodes,a quasiparticle current steeply increases by a voltage corresponding tothe sum of gap energies of both the superconducting electrodes. Thus,the current-voltage characteristic exhibits strong non-linearity.

One-bit operation of the quantum bit using superconducting devices hasbeen reported In “Nature (ENGLAND)”, Vol. 398, pp. 786-788, Apr. 29,1999. It is known that when one bit gate for controlling one bit iscombined with a two-bit gate, called a controlled-NOT gate, all ofoperations necessary for quantum computing is made possible.

Therefore, realizing a controlled-NOT gate in quantum bit usingsuperconducting devices is of extreme importance.

As shown in FIG. 1, a controlled-NOT gate has an input composed of acontrol bit and a target bit, namely, two quantum bits. Only when thestate of the control bit is “0”, the value of the target bit isinversed. Although this definition is different from the general one,where the value of the target bit is inversed only when the state of thecontrol bit is “1”, this difference gives no essential restriction.

A theoretical approach to realize a controlled-NOT gate usingsuperconducting charge quantum bits has been reported in “PhysicalReview Letters”, Vol. 79, pp. 2371-2374, Sep. 22, 1997. However, thecontrolled-NOT gate requires a large inductance to couple two quantumbits. Disadvantageously, it is difficult to realize this controlled-NOTgate,

One approach to coupling quantum bits uses capacitance. The fabricationof devices for this approach is easier than that using inductance.Furthermore, the devices for this approach can be made compact.Actually, superconducting charge quantum bits coupled by using thecapacitance have already been produced. The quantum oscillation of thequantum bits has been observed (“Nature (ENGLAND)”, Vol. 421, pp.823-826, Feb. 20, 2003).

However, any method for producing a controlled-NOT gate insuperconducting charge quantum bits coupled by using the capacitance hasnot been proposed.

SUMMARY OF THE INVENTION

In consideration of the above-mentioned circumstances, it is an objectof the present invention to provide a controlled-NOT gate insuperconducting charge quantum bits coupled by using capacitance.

According to a first aspect of the present invention, there is provideda superconducting charge quantum multi-bit device. The superconductingcharge quantum multi-bit device includes a first superconducting chargequantum bit device, a second superconducting charge quantum bit device,and an electric capacitor coupling the first and second superconductingcharge quantum bit devices.

Preferably, in the present superconducting charge quantum multi-bitdevice, each of the first and second superconducting charge quantum bitdevices has a quantum box electrode including a superconductor, acounter electrode coupled to the quantum box electrode through a tunnelbarrier, and a gate electrode coupled to the quantum box electrodethrough a gate electrostatic capacitor. Preferably, the quantum boxelectrode of the first superconducting charge quantum bit device iscoupled to the quantum box electrode of the second superconductingcharge quantum bit device through the electric capacitor.

According to a second aspect of the present invention, there is provideda controlled-NOT gate using coupled superconducting charge quantum bitsincluding first and second superconducting bit devices. In the presentcontrolled-NOT gate, each of the first and second superconducting bitdevices has a quantum box electrode including a superconductor, acounter electrode coupled to the quantum box electrode through a tunnelbarrier, and a gate electrode coupled to the quantum box electrodethrough a first electrostatic capacitor. The quantum box electrode ofthe first superconducting bit device is coupled to the quantum boxelectrode of the second superconducting bit device through a secondelectrostatic capacitor. In the present controlled-NOT gate, the gateelectrode of the second superconducting bit device further includes apulse supply unit for supplying a predetermined pulse.

Preferably, in the present controlled-NOT gate, the predetermined pulseincludes a voltage, of which peak value is determined by the firstelectrostatic capacitor of the second superconducting bit device, andthe duration of the peak value is determined by a Josephson couplingenergy produced between the corresponding superconducting box electrodeand counter electrode. The predetermined pulse may include a trapezoidalpulse. The pulse supply unit may supply a microwave pulse as thepredetermined pulse to the gate electrode of the second superconductingbit device.

According to a third aspect of the present invention, there is provideda method for generating entanglement of coupled superconducting chargequantum bits in which first and second superconducting bit devices arecoupled. Each of the first and second superconducting bit devices has aquantum box electrode including a superconductor, a counter electrodecoupled to the quantum box electrode through a tunnel barrier, and agate electrode coupled to the quantum box electrode through a firstelectrostatic capacitor. The quantum box electrode of the firstsuperconducting bit device is coupled to the quantum box electrode ofthe second superconducting bit device through a second electrostaticcapacitor.

In the present entanglement generating method, a voltage determined bythe first electrostatic capacitor is applied to the corresponding gateelectrode of each of the first and second superconducting bit devicesfor a predetermined time.

Preferably, in the present entanglement generating method, the voltagedetermined by the first electrostatic capacitor is obtained by dividingan elementary charge by the capacitance of the first electrostaticcapacitor.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a logical table of a controlled-NOT gate;

FIG. 2 is a typical circuit diagram of two superconducting chargequantum bits coupled through a capacitor;

FIGS. 3A and 3B are diagrams explaining a method for generatingentanglement according to the present invention;

FIGS. 4A and 4B show the result of a numerical calculation according toan embodiment of the present invention;

FIGS. 5A and 5B are diagrams explaining the operation of a quantumcontrolled-NOT gate according to the present invention; and

FIGS. 6A to 6F show the result of a numerical calculation according tothe present embodiment of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

An embodiment of the present invention will now be described in detailwith reference to the drawings.

FIG. 2 is a circuit diagram showing a typical example of coupledsuperconducting charge quantum bit circuits. Two superconducting chargequantum bit circuits are arranged on the right and left of the dashedline in FIG. 2, respectively. Each circuit is the same as that disclosedin Patent Document 1. According to the present embodiment, a quantum bit“0” denotes a state in which there is no excess Cooper pair in a boxelectrode and a quantum bit “1” denotes another state in which there isexcess Cooper pair. This state is controlled using a gate voltage. Aread-out electrode is provided for each of two quantum box electrodes.If different read-out technique is used, the read-out electrodes are notnecessarily needed.

The superconducting charge quantum bit circuit may also be called asuperconducting charge quantum bit device or a superconducting bitdevice. Referring to FIG. 2, the right superconducting charge quantumbit circuit is called a control quantum bit circuit 100 and the left oneis called a target quantum bit circuit 200.

The control quantum bit circuit 100 includes a first superconducting boxelectrode 101, a first counter electrode 102, a first gate electrode103, a first tunnel barrier 104, a first gate capacitor 105, a firstread-out electrode 106, and a second tunnel barrier 107.

The first superconducting box electrode 101 includes a superconductorthat becomes superconductive at a low temperature. The first counterelectrode 102 includes a superconductor which also functions as asource. The first tunnel barrier 104 includes a thin layer between thefirst superconducting box electrode 101 and the first counter electrode102. The first gate capacitor 105 is arranged between the first gateelectrode 103 and the first superconducting box electrode 101. The firstread-out electrode 106 includes a superconductor which also serves as adrain. The second tunnel barrier 107 between the first superconductingbox electrode 101 and the first read-out electrode 106 is thicker thanthe first tunnel barrier 104.

Similarly, the target quantum bit circuit 200 includes a secondsuperconducting box electrode 201, a second counter electrode 202, asecond gate electrode 203, a third tunnel barrier 204, a second gatecapacitor 205, a second read-out electrode 206, and a fourth tunnelbarrier 207.

The second superconducting box electrode 201 includes a superconductorthat becomes superconductive at a low temperature. The second counterelectrode 202 includes a superconductor that also functions as a source.The third tunnel barrier 204 includes a thin layer between the secondsuperconducting box electrode 201 and the second counter electrode 202.The second gate capacitor 205 is arranged between the second gateelectrode 203 and the second superconducting box electrode 201. Thesecond read-out electrode 206 includes a superconductor which alsoserves as a drain. The fourth tunnel barrier 207 between the secondsuperconducting box electrode 201 and the second read-out electrode 206is thicker than the third tunnel barrier 204.

As shown in FIG. 2, the first superconducting box electrode 101 iscoupled to the second superconducting box electrode 201 through abox-electrode coupling capacitor 300. Thus, the two quantum bits havethe interaction with each other.

In the following description, the right circuit serves as a control bitand the left circuit serves as a target bit.

Assuming that this quantum bits constitute one two quantum bit system,the present two quantum bit system has four states, namely, “00”, “01”,“10”, and “11”. The state “01” indicates that the first superconductingbox electrode 101 has no excess Cooper pair and the secondsuperconducting box electrode 201 has one excess Cooper pair. The state“10” indicates that the first superconducting box electrode 101 has oneexcess Cooper pair and the second superconducting box electrode 201 hasno excess Cooper pair. The state “00” denotes that the first and secondsuperconducting box electrodes 101 and 102 each have no excess Cooperpair. The state “11” denotes that the first and second superconductingbox electrodes 101 and 102 each have one excess Cooper pair.

When harniltonian of the present system is expressed as a matrix usingbases “00”, “01”, “10”, and “11, the following expression 1 is obtained.$\begin{matrix}\begin{matrix}{H = \begin{pmatrix}E_{00} & {{- \frac{1}{2}}E_{J1}} & {{- \frac{1}{2}}E_{J2}} & 0 \\{{- \frac{1}{2}}E_{J1}} & E_{01} & 0 & {{- \frac{1}{2}}E_{J2}} \\{{- \frac{1}{2}}E_{J2}} & 0 & E_{10} & {{- \frac{1}{2}}E_{J1}} \\0 & {{- \frac{1}{2}}E_{J2}} & {{- \frac{1}{2}}E_{J1}} & E_{11}\end{pmatrix}} \\{E_{nIn2} = {{E_{cl}\left( {n_{g1} - n_{1}} \right)}^{2} + {E_{c2}\left( {n_{g2} - n_{2}} \right)}^{2} + {{E_{m}\left( {n_{g1} - n_{1}} \right)} \cdot \left( {n_{g2} - n_{2}} \right)}}}\end{matrix} & (1)\end{matrix}$Where, E_(J1) and E_(J2) denote the Josephson coupling energies of thefirst and third tunnel barriers 104 and 204, respectively. E_(C1)denotes the charging energy of one Cooper pair of the firstsuperconducting box electrode 101 and E_(C2) denotes the charging energyof one Cooper pair of the second superconducting box electrode 201. Emdenotes the coupling capacitor energy between the first and secondsuperconducting box electrodes 101 and 201. This energy is defined bythe following expression 2.E _(m)=4e ² C _(m)/(CΣ1 CΣ2−C _(m) ²)  (2)Where, CΣ1 and CΣ2 denote the entire capacitances of the first andsecond superconducting box electrodes 101 and 102, respectively, andC_(m) denotes the capacitance of the box-electrode coupling capacitor300.

To increase the efficiency of a controlled-NOT gate, which will bedescribed later, it is desirable that the coupling capacitor energy belarger on condition that E_(C1)>>E_(J1) and E_(C2)>>E_(J2). n1 denotesthe number of excess Cooper pairs in the first superconducting boxelectrode 101 and n2 denotes the number of excess Cooper pairs in thesecond superconducting box electrode 201.

n_(g1) denotes the number of Cooper pairs induced in the firstsuperconducting box electrode 101 by the first gate electrode 103.Assuming that C_(g1) denotes the capacitance of the first gate capacitor105 and V_(g1) denotes a voltage applied to the first gate electrode103, n_(g1)=C_(g1)*V_(g1)/2/e, where e denotes an elementary charge.

Similarly, n_(g2) indicates the number of Cooper pairs induced in thesecond superconducting box electrode 201 by the second gate electrode203. Assuming that C_(g2) denotes the capacitance of the second gatecapacitor 205 and V_(g2) denotes a voltage applied to the second gateelectrode 203, n_(g2)=C_(g2)*V_(g2)/2/e.

FIG. 3A is a diagram showing the lowest charge energy state in ann_(g1)-n_(g2) plane. Referring to FIG. 3A, among four charge states“00”, “01”, “10”, and “11”, the energy of the state “00” is the lowestin the lower left area of four areas. Similarly, in the lower rightarea, the charge state “10” has the lowest energy. On the border betweenthe lower right and left areas, the energy of the charge state “00”equals that of the charge state “10”.

In the following description, these areas will be called as 00, 01, 10,and 11.

A method for generating entanglement will now be described.“Entanglement” means a non-local correlation that appears in an“inseparable” state of the quantum system including a plurality ofsubsystems. The inseparable state cannot be expressed by products of thesubsystem states. Entanglement, which annoyed Einstein, is a veryimportant resource peculiar to quantum information processing.Entanglement can be a key to give an advantage to quantum informationprocessing over classical information processing.

A DC voltage is applied to each of the second gate electrode 203 and thefirst gate electrode 103, so that an operating point is moved to anappropriate position (for example, a filled dot in FIG. 3A) in the area00.

Subsequently, the application of a pulse voltage to each of the secondgate electrode 203 and the first gate electrode 103 will now bedescribed. In the following description, except where specificallynoted, an ideal rectangular pulse with no rise time and no fall time asshown in FIG. 3B is considered.

Applying the pulse voltage to the first gate electrode 103 means thatthe state is shifted parallel to the axis of n_(g1) in the n_(g1)-n_(g2)plane of FIG. 3A. Applying the pulse voltage to the second gateelectrode 203 means that the state is shifted parallel to the axis ofn_(g2) in the n_(g1)-n_(g2) plane of FIG. 3A. Therefore, the pulsevoltages applied to both the gate electrodes are controlled, so that thestate can be shifted to an arbitrary point in the n_(g1)-n_(g2) plane.For example, as shown by an arrow in FIG. 3A, the state designated bythe filled dot can be shifted to a position at (n_(g1), n_(g2))=(0.5,0.5). Assuming that the coordinates of an initial operating point of thefilled dot are (n_(g1), n_(g2)), specific pulse voltages (V_(p1),V_(p2)) are obtained as V_(p1)=2*e*(0.5−n_(g1i))/C_(g1) andV_(p2)=2*e*(0.5−n_(g2i))/C_(g2).

FIG. 3B is a diagram showing system energy bands in the variation ofn_(g1) and n_(g2) along the dashed line in FIG. 3A. Typical parameters(E_(c1)=580 meV, E_(c2)=671 meV, E_(m)=96 meV) are used for acalculation. The application of the above-mentioned pulses means that aninitial state corresponding to a point A in FIG. 3B is shifted to aposition where four energy bands are the closest to each other, namely,a point at n_(g1)=(n_(g2))=0.5.

Consequently, the state starts to oscillate between the four chargestates “00”, “01”, “10”, and “11” The oscillation continues while thepulses are In the ON state. Thus, entanglement can be generated.

FIGS. 4A and 4B show the result of a calculation of the oscillationbetween the four charge states. Referring to FIG. 4A, the abscissa axisdenotes the length of a pulse. The ordinate axis denotes the square ofan absolute value of each of four coefficients c₀₀, c₀₁, c₁₀, and c₁₁for the wavefunction expressed as c₀₀|00>+c₀₁|01>+c₁₀|10>+c₁₁|11> usingthe four charge states “00”, “01”, “10”, and “11” as bases. It is foundthat the respective coefficients oscillate with the pulse length.

FIG. 4B is a plot diagram showing the strength of entanglement in timewhen time development occurs as shown in FIG. 4A. The ordinate axisdenotes amount that is called entanglement entropy. The entanglemententropy takes on values from 0 to 1. As the value is larger, theentanglement is stronger. The strength of entanglement varies over time.For example, it is found that the maximum entanglement appearsapproximately at 150 ps.

A method for implementing a controlled-NOT gate will now be described.FIG. 5A is a diagram showing the same n_(g1)-n_(g2) plane as that ofFIG. 3A.

A DC voltage is applied to each of the gate electrodes 103 and 203, sothat the operating point is moved in the vicinity of a point atn_(g1)=0.25 in the area 00 of FIG. 5A. If the operating point isslightly deviated from the point at n_(g1)=0.25, it is no problem. Ifnip is approximate to 0.5, the control bit may also be oscillated uponapplying a voltage pulse. It is undesirable.

Subsequently, the application of a pulse voltage to the second gateelectrode 203 will now be described. At that time, as shown by the arrowin FIG. 5A, the height of the pulse voltage is adjusted so that thecharge state is located on the border between the area 00 and the area01 upon applying the pulse. Assuming that the coordinates of an initialoperating point are (n_(g1l), n_(g2l)), the magnitude V_(p2) of thepulse voltage is obtained as V_(p2)=e*(1−E_(m)*n_(g1l)−2*n_(g2l)/C_(g2),This means that the peak value of the pulse voltage is defined by thecapacitance C_(g2) of the second gate capacitor 205.

Energy bands of the present system in the dashed line (n_(g1)=0.25) inFIG. 5A will now be described (FIG. 5B). It is assumed that theoperating point is located at (n_(g1), n_(g2))=(0.25, 0.2). Theabove-mentioned pulse applying operation results in the nonadiabatictransition of the initial state to n_(g2) (n_(g2L)) corresponding to acharging-energy degeneracy point of “00” and “01”.

First, a case where the initial state is “00” will now be described. Thestate “00” is located at a point A in the diagram of FIG. 5B. Due to theabovementioned pulse application, the initial state starts quantumoscillation between “00” and “01”. As is obviously understood from theenergy band diagram, the states “10” and “11” are separated from thestates “00” and “01” in terms of energy. Accordingly, the states “10”and “11” hardly contribute to the oscillation.

FIG. 6A shows the result of a calculation of the quantum oscillation. Inthe calculation, parameters for energies are set as typical typicalvalues, namely, E_(c1)=580 meV, E_(c2)=671 meV, E_(m)=190 meV, andE_(J2)=45 meV

Referring to FIG. 6A, the abscissa axis denotes the length of a pulse.The ordinate axis denotes the square of an absolute value of each of thefour coefficients c₀₀, c₀₁, c₁₀, and c₁₁ for the wavefunction expressedas c₀₀|00>+c₀₁|01>+c₁₀|10>+c₁₁|1> using the four charge states “00”,“01”, “10”, and “11” as bases. It is found that the initial state “00”oscillates between “00” and “01” in time. Oscillation period is given byh/E_(J2) (h: Planck constant). This means that the duration (pulsewidth) is determined by the Josephson coupling energy E_(J2) of thethird tunnel barrier 204, namely, the Josephson coupling energy betweenthe superconducting box electrode 201 and the counter electrode 202.

Subsequently, a case where the initial state is “10” will now bedescribed. The state “10” is located at a point C in the energy banddiagram of FIG. 5B. It is assumed that a pulse with the same height asthe foregoing case is applied to this initial state.

This pulse does not reach n_(g2H) corresponding to the charge degeneracypoint between “10” and “11”. Thus, the oscillation is suppressed. FIG.6B shows the result of a calculation. It is found that oscillationhardly occurs and the initial state “10” is held as it is.

On the basis of the above-mentioned results, the implementation of thegate operation shown in the truth table of FIG. 1 will now be described.When “00” is input, it is desirable to output “01” with a probabilityof, ideally, 1. This condition is satisfied at time shown by each arrowin FIG. 6A. The result of a calculation (not shown) obtained when theinitial state is “01” is the same as that of FIG. 6A except that c₀₀ andc₀₁ change places. Therefore, “00” is realized at the same time with aprobability of 1. In other words, the upper two operations of the truthtable in FIG. 1 are realized by the above-mentioned pulse lengths.

On the other hand, when “10” is input, oscillation hardly occurs asshown in FIG. 6B. Consequently, “10” is obtained as an output with aprobability of about 1 independent of the pulse width. When “11” isinput, the similar result is obtained. If an input state is in a generalsuperposition state, an output state is in a superposition obtained byperforming the gate operation to the each of the superposed states inthe input. Therefore, the application of the pulse having the pulsewidth shown by the arrows in FIG. 6A and having a height ofV_(p2)=e*(1−E_(m)*n_(g1i)−2*n_(g2i))/C_(g2) realizes a controlled-NOTquantum gate operation.

The amplitude of oscillation of FIG. 6B is given by E_(J2) ²/(E_(m)²+E_(J2) ²). If the value of E_(m) cannot be enough large, theoscillation amplitude becomes large. Therefore, the above-mentionedmethod is not always used, FIG. 6C shows the result of a calculationwhen E_(m) is set to 95 meV that is half that of FIG. 6B. It is foundthat a small oscillation occurs between c₁₀ and c₁₁. In this case, thedifference between oscillation periods can be used. As mentioned above,the oscillation period of FIG. 6A is given by h/E_(J2). On the otherhand, the oscillation period of FIG. 6C is given by h/(E_(m) ²+E_(J2)²)^(0.5). So long as E_(m) is not zero, these oscillation periods aredifferent from each other. FIG. 5D is a diagram obtained by replottingdata (c₀₁) shown by the dashed line in FIG. 6A and data (c₁₀) shown bythe solid line in FIG. 6C. Referring to FIG. 6D, two oscillating curvespeak approximately at the same time shown by the arrow. When a pulsehaving such a pulse width is applied to the quantum system, the desiredgate operation can be obtained.

Another alternative approach allows a pulse to have finite rise and falltimes as shown in FIG. 6E. Advantageously, the finite rise and falltimes reduce the oscillation amplitude of each of c₁₀ and c₁₁ in FIG.6C. FIG. 6F corresponds to FIG. 6C on the assumption that a trapezoidalpulse has rise and fall times each corresponding to 30 ps is used.

The oscillation amplitude of c₁₀ approximately equals 0. It can be seenthat an output corresponding to the input “10” is “10” with aprobability of about 1 independent of a pulse width. Therefore, a pulsehaving the shortest width shown by the arrows in FIG. 6F can always beused for controlled NOT. This approach has an advantage in terms offinite coherence time. As is obviously understood from FIG. 6D,unfortunately, the finite rise and fall times reduce the oscillationamplitude of c₁₀. The extent of rise and fall times to be added oradding no rise and fall times must be determined in accordance with theconditions of the actual system.

The controlled-NOT gate can use a microwave pulse in addition to theabove-mentioned voltage pulse.

Referring to FIG. 5B, the operating point is set to n_(g2)=0.2.

The microwave pulse is resonant with the energy gap between the points Aand E in FIG. 5B. The microwave pulse is applied to the system. Assumingthat an input is “00”, namely, in the point A, Rabi oscillation occursdue to the application of the microwave pulse. The oscillation occursbetween the states “00” and “01”. The period of oscillation depends onthe power of microwave pulse. The application time of microwave pulse iscontrolled in a manner similar to the above-mentioned voltage pulse,thus obtaining the state “01” as an output.

On the other hand, even if the same microwave pulse is applied to aninput “10”, namely, to the state in the point C, the microwave pulse isnot resonant with any energy gap. The state is not changed. The sameapplies to inputs “01” and “11”. Consequently, the controlled-NOTquantum gate can be implemented by the microwave pulse.

As mentioned above, according to the present invention, a controlled-NOTgate in superconducting charge quantum bits coupled by a capacitor canbe provided.

1. A superconducting charge quantum multi-bit device comprising: a firstsuperconducting charge quantum bit device; a second superconductingcharge quantum bit device; and an electric capacitor coupling the firstand second superconducting charge quantum bit devices.
 2. The deviceaccording to claim 1, wherein each of the first and secondsuperconducting charge quantum bit devices includes a quantum boxelectrode comprising a superconductor, a counter electrode coupled tothe quantum box electrode through a tunnel barrier, and a gate electrodecoupled to the quantum box electrode through a gate electrostaticcapacitor, and the quantum box electrode of the first superconductingcharge quantum bit device is coupled to the quantum box electrode of thesecond superconducting charge quantum bit device through the electriccapacitor.
 3. A controlled-NOT gate using coupled superconducting chargequantum bits including first and second superconducting bit devices,wherein each of the first and second superconducting bit devicesincludes a quantum box electrode comprising a superconductor, a counterelectrode coupled to the quantum box electrode through a tunnel barrier,and a gate electrode coupled to the quantum box electrode through afirst electrostatic capacitor, the quantum box electrode of the firstsuperconducting bit device is coupled to the quantum box electrode ofthe second superconducting bit device through a second electrostaticcapacitor, and the gate electrode of the second superconducting bitdevice further includes pulse supply means for supplying a predeterminedpulse.
 4. The controlled-NOT gate according to claim 3, wherein thepredetermined pulse includes a voltage, of which peak value isdetermined by the first electrostatic capacitor of the secondsuperconducting bit device, and the duration of the peak value isdetermined by a Josephson coupling energy produced between thecorresponding superconducting box electrode and counter electrode. 5.The controlled-NOT gate according to claim 3, wherein the predeterminedpulse includes a trapezoidal pulse.
 6. The controlled-NOT gate accordingto claim 3, wherein the pulse supply means supplies a microwave pulse asthe predetermined pulse to the gate electrode of the secondsuperconducting bit device.
 7. A method for generating entanglement ofcoupled superconducting charge quantum bits including first and secondsuperconducting bit devices, each of the first and secondsuperconducting bit devices including a quantum box electrode comprisinga superconductor, a counter electrode coupled to the quantum boxelectrode through a tunnel barrier, and a gate electrode coupled to thequantum box electrode through a first electrostatic capacitor, thequantum box electrode of the first superconducting bit device beingcoupled to the quantum box electrode of the second superconducting bitdevice through a second electrostatic capacitor, wherein a voltagedetermined by the first electrostatic capacitor is applied to thecorresponding gate electrode of each of the first and secondsuperconducting bit devices for a predetermined time.
 8. The methodaccording to claim 7, wherein the voltage determined by the firstelectrostatic capacitor is obtained by dividing an elementary charge bythe capacitance of the first electrostatic capacitor.